336 research outputs found
Electromagnetic duality in general relativity
By resolving the Riemann curvature relative to a unit timelike vector into
electric and magnetic parts, we consider duality relations analogous to the
electromagnetic theory. It turns out that the duality symmetry of the Einstein
action implies the Einstein vacuum equation without the cosmological term. The
vacuum equation is invariant under interchange of active and passive electric
parts giving rise to the same vacuum solutions but the gravitational constant
changes sign. Further by modifying the equation it is possible to construct
interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio
Non-singular black-holes on the brane
We investigate the possibility of obtaining non-singular black-hole solutions
in the brane world model by solving the effective field equations for the
induced metric on the brane. The Reissner-Nordstrom solution on the brane was
obtained by Dadhich etal by imposing the null energy condition on the 3-brane
for a bulk having non zero Weyl curvature. In this work, we relax the condition
of vanishing scalar curvature , however, retaining the null condition. We
have shown that it is possible to obtain class of static non-singular
spherically symmetric brane space-times admitting horizon. We obtain one such
class of solution which is a regular version of the Reissner-Nordstrom solution
in the standard general relativity.Comment: 8 pages, References added, Version to appear in Int. J. Mod. Phys.
A spacetime dual to the NUT spacetime
By decomposing the Riemann curvature into electric and magnetic parts, a
duality transformation, which involves interchange of active and passive
electric parts, has recently been proposed. It was shown that the Schwarzschild
solution is dual to the one that describes the Schwarzschild particle with
cloud of string dust or a global monopole. Following the same procedure we
obtain the solution dual to the NUT spacetime.Comment: 10 pages, Latex. Accepted for publication in Classical and Quantum
Gravit
Collapsing sphere on the brane radiates
We study the analogue of the Oppenheimer-Snyder model of a collapsing sphere
of homogeneous dust on the Randall-Sundrum type brane. We show that the
collapsing sphere has the Vaidya radiation envelope which is followed by the
brane analogue of the Schwarzschild solution described by the
Reissner-Nordstrom metric. The collapsing solution is matched to the brane
generalized Vaidya solution and which in turn is matched to the
Reissner-Nordstrom metric. The mediation by the Vaidya radiation zone is the
new feature introduced by the brane. Since the radiating mediation is
essential, we are led to the remarkable conclusion that a collapsing sphere on
the brane does indeed, in contrast to general relativity, radiate null
radiation.Comment: Minor changes, main results remain unchanged, to appear in Phys.
Lett.
Gravitational Collapse in Constant Potential Bath
We analyse here the gravitational collapse of directed null radiation in a
background with a constant potential such as one produced by a star system like
galaxy in which the collapsing object is immersed. Both naked singularities and
black holes are shown to be developing as the final outcome of the collapse. An
interesting feature that emerges is that a part of the naked singularity
spectrum in collapsing Vaidya region gets covered in the corresponding
dual-Vaidya region, which corresponds to the Vaidya directed null radiation
sitting in constant potential bath. The implications of such a result towards
the issue of stability of naked singularities are discussed.Comment: LaTex 12 Pages, 2 figures. To appear in Physical Review
On the enigmatic - a true constant of spacetime
Had Einstein followed the Bianchi differential identity for the derivation of
his equation of motion for gravitation, would have emerged as a true
new constant of spacetime on the same footing as the velocity of light? It is
then conceivable that he could have perhaps made the most profound prediction
that the Universe may suffer accelerated expansion some time in the future!
Further we argue that its identification with the quantum vacuum energy is not
valid as it should have to be accounted for like the gravitational field energy
by enlarging the basic framework of spacetime and not through a stress tensor.
The acceleration of the expansion of the Universe may indeed be measuring its
value for the first time observationally.Comment: 4 pages, a comprehensive revision with much refinement and new
insights, more references adde
Inhomogeneous imperfect fluid spherical models without Big-Bang singularity
So far all known singularity-free cosmological models are cylindrically
symmetric. Here we present a new family of spherically symmetric non-singular
models filled with imperfect fluid and radial heat flow, and satisfying the
weak and strong energy conditions. For large anisotropy in pressure and
heat flux tend to vanish leading to a perfect fluid. There is a free function
of time in the model, which can be suitably chosen for non-singular behaviour
and there exist multiplicity of such choices.Comment: 8 pages, LaTeX versio
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